A head-mounted display (hereafter “HMD”) is a device that displays information to a user in a state of being mounted on the head of the user. In terms of mounting on the head, generally it is preferable that the HMD is compact and light, but in terms of display performance, it is preferable that the screen is large and image quality is high. In conventional HMDs, there is a method of optically magnifying an image displayed on a compact liquid crystal panel or the like using a convex lens, a free-form surface prism or the like, so that an expanded fictive image is displayed to the user (e.g. see Japanese Patent Unexamined Publication No. H8-240773). This method of magnifying images with a prism is called an “optical magnification method” in this specification.
In a display device using a computer generated hologram (hereafter “CGH”), a diffraction pattern, which is calculated by a computer using an image to be displayed as input data, is displayed on a phase modulation type liquid crystal panel as a CGH, and laser light is irradiated onto the liquid crystal panel and is diffracted, whereby the wavefront of the display light from the fictive image position is reproduced, and the fictive image is displayed to the user (e.g. see Japanese Translation of PCT Application No. 2008-541145). According to the display device with a CGH, it is possible to omit a prism and the like which have been required in the conventional HMD with an optical magnification method for magnifying images. Hence, it becomes possible to realize a more compact and lighter HMD by reducing the size of the optical system.
A method of displaying an image using CGH is briefly described hereinafter. In the display device of CGH method, a diffraction pattern is computed from an image to be displayed. In general, in computing a diffraction pattern, a method is used such as generating a diffraction pattern from an image to be displayed to the user (hereafter “original image”) using a generation method based on a point filling method or a Fourier transform.
FIG. 34 is a diagram showing examples of an original image and a diffraction pattern computed from the original image. In FIG. 34, the original image 401 is an example of an original image, and the diffraction pattern 402 is an example of a diffraction pattern generated from the original image 401. This diffraction pattern 402 is displayed on a phase modulation type liquid crystal panel or the like as a CGH, and a diffraction light is generated by illuminating the liquid crystal panel with laser light. Consequently, the user can visually recognize the original image 401, based on which the diffraction pattern 402 is generated, as a diffraction light from the diffraction pattern 402 on the liquid crystal panel.
Next, an example of a computation method to generate a diffraction pattern using the point filling method will be described. In the case of the point filling method, an original image (object) is regarded as a set of point light sources, and a diffraction pattern is computed from a phase when the light from each point light source overlaps at each point on the liquid crystal panel.
FIG. 35 is a diagram depicting an example of a positional relationship between an original image 501 and a liquid crystal panel 502 that displays a diffraction pattern on generating the diffraction pattern. In order to generate the diffraction pattern to be displayed on the liquid crystal panel 502 using the point filling method, each point (each pixel) on the original image 501 is regarded as a point light source, as described above. If a point i on the original image 501 has an amplitude ai and a phase φi, a complex amplitude of the light generated from this point i, observed at a point u on the liquid crystal panel 502, is given by the following Expression (1).
                                          u            i                    ⁡                      (                          ξ              ,              η                        )                          =                                            a              i                                      r              i                                ⁢          exp          ⁢                      {                          -                              j                ⁡                                  (                                                            kr                      i                                        +                                          ϕ                      i                                                        )                                                      }                                              (        1        )            
Further, ri in Expression (1) denotes a distance between the point i and the point u, and ri is computed by the following Expression (2), where the origin is the center of the liquid crystal panel 502, the coordinates of the point i are (xi, yi, zi), and the coordinates of the point u are (ξ, η, 0).ri=√{square root over ((ξ−xi)2+(η−yi)2+zi2)}{square root over ((ξ−xi)2+(η−yi)2+zi2)}  (2)
Further, k in Expression (1) denotes a wave number, and is given by k=2π/λ, where λ denotes a wavelength of the light from the point i. The complex amplitude of the light from the point i is determined at the point u by the computation using Expression (1). Hence, the same computation is performed at each point on the original image 501, and the results are added, whereby the value of the complex amplitude at the point u on the liquid crystal panel 502 can be determined. It is to be noted that the phase value of the point i is given by adding random phase values to the original image 501. Expression (3) is an expression to indicate a complex amplitude at the point u.
                              u          ⁡                      (                          ξ              ,              η                        )                          =                              ∑                          i              =              1                        N                    ⁢                                          ⁢                                    u              i                        ⁡                          (                              ξ                ,                η                            )                                                          (        3        )            
In the point filling method, a diffraction pattern is generated by performing computation of Expression (3) for each point on the liquid crystal panel 502. In this example, a phase variation, by a reference light, or the like is not illustrated to simplify description. As described above, by computing a diffraction pattern using the point filling method, it becomes possible to reproduce a wavefront of a display light from an arbitrary object. Therefore, a position of a reconstructed image (fictive image) can be controlled, even without such an optical component as a prism, as in the case of the conventional optical magnification method.
One of the problems of the CGH method is the computing volume of a diffraction pattern. In the case of the point filling method, the computing volume dramatically increases depending on the number of pixels of the original image and the number of pixels of a liquid crystal panel to display a diffraction pattern. Therefore, a proposed technique is computing a diffraction pattern using an approximation for a distance between a point on an object and a point on a liquid crystal panel, and performing inverse Fourier transform on data generated by assigning a random phase value to each pixel of the original image data (e.g. Japanese Patent Publication No. 4795249). In a case where the number of pixels of original image data is N×N and the number of pixels of a diffraction pattern is N×N, an order of the computation of the point filling method is the fourth power of N, but with a technique to use inverse Fourier transform, an order of the computation is reduced to a square of (N×log N).
However, in a case where a diffraction pattern is computed by inverse Fourier transform and the like, in order to reduce computation volume, it becomes difficult to freely set a position of a reconstructed image (distance from the liquid crystal panel) by CGH, since approximation is used for computing the distance between the object (original image) and the liquid crystal panel. As a rule, in a case where a diffraction pattern is computed by inverse Fourier transform and a liquid crystal panel for displaying a diffraction pattern as a CGH is illuminated with parallel light, a reconstructed image by CGH is reconstructed based on the assumption that this image is located at infinity from the liquid crystal panel. A method that can be used for solving this problem is performing further computation for correcting the computation result based on inverse Fourier transform.
FIG. 36 shows an example of a diffraction pattern correction. A diffraction pattern 601 is a basic diffraction pattern generated by performing inverse Fourier transform on an original image. In a case where this basic diffraction pattern 601 is displayed on a liquid crystal panel, the reconstructed image is reconstructed in a position at infinity. A correction pattern 602 is a correction pattern for correcting the position of the reconstructed image of the basic diffraction pattern 601. In the case of FIG. 36, the correction pattern 602 is generated by computing a phase in the case when the wavefront of the spherical wave from the point light source, which is virtually disposed in a position to display the reconstructed image, enters the liquid crystal panel.
A composite diffraction pattern 603 is a diffraction pattern generated by superposing the basic diffraction pattern 601 and the correction pattern 602. In a case where the composite diffraction pattern 603 is displayed on the liquid crystal panel, the position of the reconstructed image becomes the position of the point light source that was used for generating the correction pattern 602. The computation cost to superpose the correction pattern 602 on the basic diffraction pattern 601 is sufficiently low, compared with the case of the point filling method or the like. Therefore, using this technique makes it possible to control the position of the reconstructed image while computing the diffraction pattern at high-speed.
Another problem of a CGH type display device is quantization noise. Generally, in a case where a diffraction pattern is computed using the point filling method or inverse Fourier transform after adding a random phase value to each pixel of an original image, each pixel of the diffraction pattern is represented by a complex number having a phase in the range from 0 to 2π. However, in a case where the liquid crystal panel can express only specific phase values, data of each pixel of the diffraction pattern must be quantized to a CGH that can be displayed on the liquid crystal panel.
For example, in a case of using a liquid crystal panel constituted by ferroelectric liquid crystals, phase values that can be expressed by this liquid crystal panel are limited to 0 or π. Therefore, in displaying a diffraction pattern as CGH on the liquid crystal panel, a value of each pixel must be binarized to 0 or π. In a case where this kind of quantization is performed, the information volume of the original diffraction pattern is diminished. As a result, a noise called “quantization noise” is generated in the reconstructed image based on CGH.
A method used for handling this problem is suppressing the noise generation by applying an error diffusion technique when the diffraction pattern computed from the original image is quantized to the phase values that can be displayed on the liquid crystal panel (e.g. Estimation of optimal error diffusion for computer-generated holograms, Ken-ichi Tanaka, Teruo Shimomura Kyushu Institute of Technology (Japan) Proc. SPIE 3491, 1998 International Conference on Applications of Photonic Technology III: Closing the Gap between Theory, Development, and Applications, 1017 (Dec. 4, 1998); doi: 10.1117/12.328674). Here, error diffusion is a technique to disperse error generated during quantization (difference between a pixel value before quantization and a pixel value after quantization) into peripheral pixels. The amount of errors to be dispersed to the peripheral pixels differs depending on the error diffusion technique, but a technique to perform weighting as shown in FIG. 37, for example, has been proposed (Floyd-Steinberg method).
FIG. 37 shows an example of the error diffusion coefficients used for error diffusion. FIG. 37 shows a 3×3 matrix of which center is a quantization pixel, where the quantization is performed. According to FIG. 37, 7/16 of the error is added to the pixel located to the right of the quantization pixel, and 5/16 of the error is added to the pixel located below the quantization pixel. By propagating the error to peripheral pixels like this, the generated noise can be concentrated to a high frequency area.
FIG. 38 shows an example of a diffraction pattern of which error diffusion was performed and an example of a diffraction pattern of which error diffusion was not performed, during quantization. In FIG. 38, a diffraction pattern 801 is an example of a diffraction pattern after quantization when error diffusion was not performed, and a diffraction pattern 802 is an example of a diffraction pattern after quantization when error diffusion was performed. By performing error diffusion, the quantization noise can be concentrated to a high frequency area of CGH. In the reconstructed image, the high frequency area of CGH corresponds to the edge portions of the display screen. Therefore, the quantity of the quantization noise on the entire display screen does not change depending on whether error diffusion is performed, but the generation of the quantization noise at the center portion of the display screen can be suppressed by error diffusion.
In this way, in a CGH type display device, methods for improving image quality by optimizing the position of a reconstructed image (fictive image) and suppressing the quantization noise, while keeping computation volume low, are now under research.